Information on Result #1053193
Linear OOA(2158, 1027, F2, 4, 27) (dual of [(1027, 4), 3950, 28]-NRT-code), using OOA 4-folding based on linear OA(2158, 4108, F2, 27) (dual of [4108, 3950, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2158, 4109, F2, 27) (dual of [4109, 3951, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2158, 1027, F2, 4, 26) (dual of [(1027, 4), 3950, 27]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2159, 1027, F2, 4, 27) (dual of [(1027, 4), 3949, 28]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2160, 1027, F2, 4, 27) (dual of [(1027, 4), 3948, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(2158, 1027, F2, 5, 27) (dual of [(1027, 5), 4977, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2158, 1027, F2, 6, 27) (dual of [(1027, 6), 6004, 28]-NRT-code) | [i] | ||
| 6 | Linear OOA(2158, 1027, F2, 7, 27) (dual of [(1027, 7), 7031, 28]-NRT-code) | [i] | ||
| 7 | Linear OOA(2158, 1027, F2, 8, 27) (dual of [(1027, 8), 8058, 28]-NRT-code) | [i] | ||
| 8 | Digital (131, 158, 1027)-net over F2 | [i] | ||